A comparative study of tests for the difference of two Poisson means

We investigate different test procedures for testing the difference of two Poisson means. Asymptotic tests, tests based on an approximate p-value method, and a likelihood ratio test are considered. Size and power performance of these tests are studied by means of Monte Carlo simulation under different settings. If one wants to control the actual significance level at or below the pre-chosen nominal level, tests based on approximate p-value method are the desirable candidates. If one allows tests whose actual significance levels may occasionally exceed the pre-chosen nominal level by an acceptable margin, asymptotic tests based on an unbiased estimate and constrained maximum likelihood estimate are reasonable alternatives. We illustrate these testing procedures with a breast cancer example.